1. Quality Improvement PowerPoint presentation to accompany Besterfield, Quality Improvement, 9e PowerPoint presentation to accompany Besterfield, Quality Improvement, 9e Chapter 11- Reliability

2. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 2 Outline   Fundamental Aspects   Additional Statistical Aspects   Life and Reliability Testing Plans   Test Design   Availability and Maintainability

3. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 3 When you have completed this chapter you should be able to:  Know the definition of reliability and the factors associated with it.  Know the various techniques to obtain reliability.  Understand the probability distributions, failure curves, and reliability curves as a factor of time. Learning Objectives

4. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 4 When you have completed this chapter you should be able to:  Calculate the failure rate under different conditions.  Construct the life history curve and describe its three phases.  Calculate the normal, exponential, and Weibull failure rate. Learning Objectives cont’d.

5. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 5 When you have completed this chapter you should be able to:  Construct the OC Curve  Determine life and reliability test curves  Calculate the normal, exponential, and Weibull failure rate  Understand the different types of test design  Understand the concepts of availability and maintainability Learning Objectives cont’d.

6. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 6  Generally defined as the ability of a product to perform as expected over time.  Formally defined as the probability that a product, piece of equipment, or system will perform its intended function for a prescribed life under stated environmental conditions Reliability

7. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 7  Means quality over the long run.  A product that “works” for a long period of time is a reliable one.  Since all units of a product will fail at different times, reliability is a probability. Reliability

8. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 8 There are four factors associated with Reliability: 1. Numerical Value.  The numerical value is the probability that the product will function satisfactorily during a particular time. Reliability

9. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 9 There are four factors associated with Reliability: 2. Intended Function.  Product are designed for particular applications and are expected to be able to perform those applications. Reliability

10. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 10 There are four factors associated with Reliability: 3. Life.  How long the product is expected to last. Product life is specified as a function of usage, time, or both. Reliability

11. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 11 There are four factors associated with Reliability: 4. Environmental Conditions  Indoors.  Outdoors.  Storage.  Transportation. Reliability

12. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 12 Emphasis: 1. The Consumer Protection Act of 1972. assist consumers in evaluating the comparative safety of consumer products; to develop uniform safety standards for consumer products and to minimize conflicting state and local regulations; and to promote research and investigation into the causes and prevention of product related death, illnesses, and injuries. 2. Products are more complicated. 3. Automation. Achieving Reliability

13. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 13  As products become more complex (have more components), the chance that they will not function increases.  The method of arranging the components affects the reliability of the entire system.  Components can be arranged in series, parallel, or a combination. System Reliability

14. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 14 R S = R 1 R 2... R n 12n  For a series systems, the reliability is the product of the individual components.  As components are added to the series, the system reliability decreases. Series System

15. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 15 R s = 1 - (1 - R 1 ) (1 - R 2 )... (1 - R n ) 1 2 n  When a component does not function, the product continues to function, using another component, until all parallel components do not function. Parallel System

16. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 16  Convert to equivalent series system AB C C D RARARARA RBRBRBRB RCRCRCRC RDRDRDRD RCRCRCRC AB C’ C’D RARARARA RBRBRBRB RDRDRDRD R C’ = 1 – (1-R C )(1-R C ) Series-Parallel System

17. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 17  The most important aspect of reliability is the design.  It should be as simple as possible.  The fewer the number of components, the greater the reliability.  Another way of achieving reliability is to have a backup or redundant component (parallel component). Design

18. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 18  Reliability can be achieved by overdesign.  The use of large factors of safety can increase the reliability of a product.  When an unreliable product can lead to a fatality or substantial financial loss, a fail-safe type of device should be used. Design

19. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 19  The second most important aspect of reliability is the production process.  Emphasis should be placed on those components which are least reliable.  Production personnel. Production

20. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 20  The third most important aspect of reliability is the transportation.  Packaging  Shipment  Performance of the product by the customer is the final evaluation.  Good packaging techniques and shipment evaluation are essential. Transportation

21. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Maintenance  Eliminate need  Warnings, such as audible or visual signals  Simple and easy to perform 21

22. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 22 Distributions Applicable to Reliability:  Exponential distribution.  Normal distribution.  Weibull distribution. Reliability Curves:  The curves as a function of time. Additional Statistical Aspects

23. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 23 Reliability Curves:  The reliability curves for the exponential, normal and Weibull distributions as a function of time are given in Fugure 11-2(b). Additional Statistical Aspects

24. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Exponential Normal Weibull 24

25. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 25 Failure-Rate Curve:  It is important in describing the life-history curve of a product.  See Figure 11-2c. Additional Statistical Aspects

26. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Exponential Normal Weibull 26

27. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 27  The curve, sometimes referred to as the “bathtub” curve, is a comparison of failure rate with time.  It has three distinct phases:  The debugging phase.  The chance failure phase.  The wear-out phase. Life History Curve

28. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 28 “Infant mortality period” Debugging Phase Chance Failure Phase Wear Out Phase Life History Curve

29. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 29 1. The debugging phase: It is characterized by marginal and short-life parts that cause a rapid decrease in the failure rate. It may be part of the testing activity prior to shipment for some products. The Weibull distribution ß<1 is used to describe the occurrence of failures. Life History Curve

30. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 30 2. The chance failure phase: Failures occur in a random manner due to the constant failure rate. The Exponential and the Weibull distributions β= 1 are best suited to describe this phase. 3. The wear-out phase: Is depicted by a sharp raise in failure rates. The Normal distribution and the Weibull distribution ß >1 are used to describe this phase. Life History Curve

31. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 31  The Weibull distribution is usually used.  The Normal distribution. R(t): Reliability at time t P(t): Probability of failure or area of the normal curve to the left of time t. Table A. Normal Failure Analysis

32. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 32 Exponential distribution: R t = e –t/ө Where: t: Time or cycles. ө: Mean life. Exponential Failure Analysis

33. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 33  Can be used for the debugging phase (ß<1) and the chance failure phase (ß=1).  By setting = 1, the Weibull equals the exponential.  By setting ß=3.4, the Weibull approximates the Normal. Rt = e –(t/ө)ß Where ß is the Weibull slope. Weibull Failure Analysis

34. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 34 Steps: 1. Assume values for the mean life ө. 2. These values are converted to the failure rate, λ =1/ө. 3. Calculate the expected average number of failures nTλ. 4. From Table C of the Appendix using nTλ and c value, get P a. 5. See Table 11-1 OC Curve Construction

35. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 35 FIGURE 11-4 OC Curve for the Sampling Plan, n = 16, T = 600 h, c = 2, and r = 3

36. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 36 Type of Tests:  Failure-Terminated: These life-test sample plans are terminated when a preassigned number of failures occurs to the sample.  Time-Terminated: This life-test sampling plan is terminated when the sample obtains a predetermined test time. Life and Reliability Testing Plans

37. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 37 Type of Tests cont’d.:  Sequential: A third type of life-testing plan is a sequential life-test sampling plan whereby neither the number of failures nor the time required to reach a decision are fixed in advance. Life and Reliability Testing Plans

38. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 38 Tests are based on one or more of the following characteristics:  Mean life: the average life of the product.  Failure rate: the percentage of failures per unit time or number of cycles.  Hazard rate: the instantaneous failure rate at a specified time.  Reliable life: the life beyond which some specified portion of the items in the lot will survive. Life and Reliability Testing Plans

39. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 39 Test are based on one or more of the following characteristics cont’d.:  Hazard rate: the instantaneous failure rate at a specified time.  Reliable life: the life beyond which some specified portion of the items in the lot will survive. Life and Reliability Testing Plans

40. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 40  Quality Control Reliability Handbook H108 gives sampling procedures and tables for life and reliability testing.  Sampling plans in the handbook are based on the exponential distribution.  Provides for the three different types of test: failure-terminated, time-terminated, and sequential. Handbook H108

41. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 41  The handbook is over 70 pages long.  The time-terminated plan: 1. Stipulated producer’s risk, consumer’s risk, and sample size. 2. Stipulated producer’s risk, rejection number, and sample size. 3. Stipulated producer’s risk, consumer’s risk, and test time. Handbook H108

42. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Test Design  High statistical confidence in a reliability measure with tests of a reasonable size and length is difficult  Accelerated life testing (ALT) provide this solution or give an early warning  There are three types: Use-rate acceleration Product aging acceleration Product stress acceleration 42

43. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 43 For long-lasting products and services such as refrigerators, electric power lines, and front-line services, the time-related factors of availability, reliability, and maintainability are interrelated. Availability and Maintainability

44. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 44  It is a time-related factor that measures the ability of a product or service to perform its designated function.  The product or service is available when it is in the operational state, which includes active and standby use. Availability

45. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 45 Where: MTBM = mean time between maintenance MDT = mean down time MTBF = mean time between failures MTTR = mean time to repair Availability

46. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 46 Maintainability is the probability that a system or product can be retained in, or one that has failed can be restored to, operating condition in a specified amount of time. Maintainability

47. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 47  Maintainability is the totality of design factors that allows maintenance to be accomplished easily.  Preventive maintenance reduces the risk of failure.  Corrective maintenance is the response to failures. Maintainability

48. Quality Improvement, 9e Dale H. Besterfield © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Computer Program  EXCEL/minitab solves for exponential and Weibull distributions.  EXCELminitab program files on the website solve β and using the file name Weibull 48